140 PROCEEDINGS OF THE AMERICAN ACADEMY. 



copper surfaces, in contact with the water, the temperatures t + 0.82 and 

 t — 0.82 respectively. This makes each copper coating to have a tem- 

 perature gradient of 0°.l per cm., with a difference of 3°. 18 between its 

 outer surface and the water stream flowing across it. The ratio of the 



u 



^2 



temperature gradient to the external difference is therefore about 



According to this we may infer that a stream of water flowing across 

 one face of a copper wire, with a speed equal to that of the flow across 

 the surface of our disk, and with a temperature t degrees above the tem- 

 perature of the face of the wire, will maintain within that wire a gradient 

 of temperature equal to ^ -f- 32, all lateral action being excluded. 



The point of attachment of the platinum wire to the copper is about 

 midway of the exposed part of the copper, and is as much as 3.0 cm. 

 from the outer end of the plug. If the copper wire terminated at this 

 point of attachment, and suffered conductive contact with the water only 

 at its terminal surface, the change of temperature from the outer end of 

 the plug, supposed non-conductive, to the end of the wire would accord- 

 ingly be about ^^, ^^, as great as the difference of temperature between 

 the end of the wire and the water flowing past it. If, therefore, the wire 

 at the outer end of the plug exceeds in temperature the stream ol water 

 by 0°.5, as we will assume, the fall of temperature within the wire would 

 be about 0°.04, and the end of the wire would be about 0'^.46 above the 

 temperature of the stream. This conclusion, however, is based on a 

 false assumption as to the area of contact of the wire with the water ; in 

 fact, this area of contact is about sixty times as great as the cross-section 

 of the wire, and the point of attachment of the platinum is near the 

 middle of this area, so that we shall not be very far from the truth in 

 assuming that the temperature of the copper at the cross-section next the 

 point of attachment of the platinum is the same that it would be if the 

 wire had contact with the water only at this cross-section but had sixty 

 times as great a surface conductivity as such an area really has in contact 

 with the stream. This leads to the conclusion that the fall of temper- 

 ature within the wire, from the outer end of the plug to the point of 

 attachment of the platinum, is about f ^ times as great as the difference of 

 temperature between the point of attachment and the stream. This last 

 difference would therefore be rather less than 0°.l, but we will call it 

 that. 



The problem now is to find how much the mean temperature of a plat- 

 inum wire 0.012 cm. in diameter and 11 cm. long will exceed that of the 

 water stream in which it is placed, if one end of this wire is kept 0°.l 

 above the temperature of the water. This problem is of a faiuiliar sort, 



